Speculation

Pierce refers to himself as a Doctor[2], while Digdoug uses quotation marks when referring to "Doctor" Herbert Sassafras.[3] It may be that it's a title that's conferred and frequently falsified by young, inexperienced, or unethical healomancers.

Natural Healomancy

The healing of a unit's wounds at the beginning of their turn likely represents some form of Natural Healomancy.